# The flexure of infinite rectangular plates of varying thickness

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## Conclusion

It will be seen that the deflection and moment *M*_{x} are both zero on edges *x*=±*a*, ±3 *a*,... Hence the above solution is also valid for a plate of finite length simply supported on any two of these edges.

*MacGregor's*single concentrated load case is concerned, the loading is written in the

*Fourier*integral form

*Fourier*integral

The evaluation of this integral must be performed numerically after the value of the thickness constant *b* has been selected to best fit the actual variation. This may be done by computing the integrand over a certain range for various values of *γa* and evaluating the integral in this range by *Simpson*'s rule.

Beyond this range, the integrand may be written in simpler form and the integral evaluated in closed form. This involves considerable labor and, since the calculations must be repeated for each value of *b* selected, they will not be made here. Numerical calculations of *Fourier* integrals such as the above have been made by *Girkmamn*^{7} and the author^{8}.

### Keywords

Neural Network Fourier Complex System Numerical Calculation Information Theory## Preview

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